For the close coil helical spring of the maximum deflection is A. $$\frac{{{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$ B. $$\frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$ C. $$\frac{{4{{\text{W}}^2}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$ D. $$\frac{{8{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{n}}}}$$

The correct answer is $\frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$.

The maximum deflection of a close coil helical spring is given by the following equation:

$$\delta = \frac{{2{\text{W}}{{\text{D}}^3}{\text{n}}}}{{{{\text{d}}^4}{\text{N}}}}$$

where:

• $\delta$ is the maximum deflection,
• $W$ is the load applied to the spring,
• $D$ is the mean coil diameter,
• $n$ is the number of active coils,
• $d$ is the wire diameter, and
• $N$ is the spring rate.

The spring rate is a measure of how much the spring will deflect under a given load. It is calculated by the following equation:

$$N = \frac{{F}}{{\delta}}$$

where:

• $F$ is the force applied to the spring, and
• $\delta$ is the deflection of the spring.

The maximum